Abstract

When a mining company begins extraction from a finite resource, it does so in the
presence of numerous uncertainties. One key uncertainty is the future price of the
commodity being extracted, since a large enough drop in price can make a resource
no longer cost-effective to extract, resulting in the mine being closed down. By specifying
a stochastic price process, and implementing a financial-type model which
leads to the use of partial differential equations, this paper creates the framework
for efficiently capturing the probability of a mine remaining open throughout its
planned extraction period, and derives the associated expected lifetime of extraction.
An approximation to the abandonment price is described, which enables a
closed-form solution to be derived for the probability of operational success and expected
lifetime. This approximation compares well with the full solution obtained
using a semi-Lagrangian numerical technique.